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Margie is a trusted home cook immersed in German foodways.
Pecorino or grana padana
pierino is a trusted source on General Cooking and Tough Love.
I'd go with grana here also as it's a similar type of cheese. Pecorino though is a sheep's milk cheese with a much sharper flavor.
Aged asiago or fontina
QueenSashy is a trusted home cook.
I think it will very much depend on what you are making. Grana padano is the same family, but the taste will never come close to a good Parmesan. Pecorino is an entirely different taste, but contributes to a dish in its own way.
If I don't have any grating cheese at all, I will top pasta with bread crumbs fried in olive oil and salted, as per Italian peasants. It gives a nice savory pop.
Quinciferous, that is sooo true. I also make olive oil fried bread crumbs with garlic. Cannot get better (and simpler than that)!
Keep wine & water cool all day (yes, even at the beach).
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